#ATTENDANCE QUIZ for Lecture 7 of Math251(Dr. Z.)
#EMAIL  RIGHT AFTER YOU WATCHED THE VIDEO
#BUT NO LATER THAN  Sept. 28, 2020, 8:00PM (Rutgers time)
#THIS .txt FILE (EDITED WITH YOUR ANSWERS)
#TO:
#DrZcalc3@gmail.com
#Subject: aq7
#with an ATTACHMENT CALLED:
#aq7FirstLast.txt
#(e.g. aq7DoronZeilberger.txt)




#LIST ALL THE ATTENDANCE QUESTIONS FOLLOWED BY THEIR ANSWERS

Question 1:
Let a:= 5th digit of RUID b:= 2nd digit of RUID
Let f(x,y):= x^a +b*a^(2*a)*y^3
Find partial derivatives of f(x,y)

Answer 1:
a=0 b=9
f(x,y)=x^0 + 9*0^(2*0)*y^3
f_x=0+0
f_y=0+0


Question 2:
With same a=0 and b=9 as above
find implicit of both x and y
x^a * y^2 * z^b + x^2*y^(3*b)*z^3=exp(x*y*z)

Answer 2:
x^0 * y^2 * z^9 + x^2*y^(3*9)*z^3=exp(x*y*z)
x: y^2(1*9z^8dz/dx+0*z^9)+y^(27)(x^2*3z^2dz/dx+2x*z^3)=exp(y(xdz/dx+z))=exp(yxdz/dx+yz)
x: y^2(9z^8dz/dx)+y^(27)(x^2*3z^2dz/dx+2x*z^3)=exp(yxdz/dx+yz)
y:x^0(y^2*9z^8dz/dy+2y*z^9)+x^2(y^27*3z^2*dz/dy+27y^26*z^3)=exp(x(y*dz/dy+z))
y:(y^2*9z^8dz/dy+2y*z^9)+x^2(y^27*3z^2*dz/dy+27y^26*z^3)=exp(xydz/dy+xz)


Question 3:
Find f_y(1,1) of
x^2+y^2 = x*y*z + x*y*z^5 

Answer 3:
2y=x(ydz/dy+z) + x(y*5z^4dz/dy+1*z^5)
2=(dz/dy)+1 + (5dz/dy)+1
0=dz/dy


Question 4: 
Is f_y(1,1)=0

Answer 4:
yes it does, I couldn't predict it b/c slopes are different


Question 5:
Let a and b be as above
Find equation of tangent plane to surface
z= x^a + y^b +a*b*x*y At point (1,2,2+a*b)

Answer 5:
z= x^0 + y^9 + 0*x*y At point (1,2,2+0)
Does 2= 1+2^9+0 NO so refuse problem